ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   167.   78.2 Green     
 2     2   173.   87.3 Grey      
 3     3   162.   86.5 Brown     
 4     4   164.   73.9 Green     
 5     5   175.   89.0 Grey      
 6     6   164.   80.4 Brown     
 7     7   181.   85.2 Blue      
 8     8   169.   74.5 Green     
 9     9   171.   84.2 Green     
10    10   165.   89.8 Brown     
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1] -1.491336314 -0.304440763 -0.159751420  0.148774272 -0.616522602
   [6] -1.391150494  1.364045336  1.380223020  0.345080475  1.664469963
  [11]  0.015902355 -0.158024720 -0.263870388  0.003009437  0.127551269
  [16] -0.318741031  2.308503924  0.679154727  2.007564674  0.351276484
  [21] -1.299721902 -0.910940484  1.037855096  0.648024372  0.026133115
  [26]  1.848418060 -0.829614061  0.344085767 -1.418493338  1.115235696
  [31] -0.029164432  1.130181600 -1.627462579  0.174395275  1.008839418
  [36] -1.547084409  0.363307602  2.039672146 -0.475166217 -2.231522027
  [41]  1.159577864 -0.690387799  0.025346041 -1.316056566  0.795906627
  [46]  0.261045564  0.120450084  1.982727872  0.854097971 -0.126099475
  [51]  0.472127030 -0.842078003  0.328857843 -0.617634070 -1.998531003
  [56]  0.088357487  0.755272398  0.662870362 -0.748936899  1.195536069
  [61]  0.960938884  1.172827015  1.177953857  0.571574325  0.454128959
  [66] -0.574192274 -1.625603015  0.032838839  0.416283525 -1.215016863
  [71] -0.261221006  0.996382336 -0.044527725  0.198164845 -0.372011777
  [76]  1.024907592  0.993887773  0.141702670  1.523662131 -0.751270031
  [81] -0.001587115 -0.740790667 -1.142751408  0.141575501  0.496128377
  [86] -1.173454368  0.311329909  0.736035280 -0.280371919  0.764649191
  [91] -0.082388714  0.102570295  0.396124896 -0.639962108  0.367898646
  [96] -0.170554976 -1.464740900  1.157762093 -0.823104021 -0.715556968
 [101]  3.014318587 -0.451572724 -0.783615023  2.232986573  0.164240007
 [106]  1.430858397 -0.075945780  0.978793361  0.361029869 -0.329221004
 [111] -1.531470042  0.966807670 -0.955358324  1.029685217 -1.329440759
 [116]  0.476882892  0.263295848 -0.049652383 -0.472708655 -0.104363811
 [121] -0.243431623  0.031526480  1.917842213 -0.624496177 -1.097009538
 [126]  1.496738571  0.382547995  0.620836434 -0.723691935  0.811068947
 [131]  0.373606951 -0.202574190  0.417858672 -2.137359842  0.310639050
 [136]  0.407650521 -0.923123756 -0.528550637 -0.511957549 -0.075236046
 [141] -0.966893389  0.451964376 -0.665989402 -1.053508461 -2.487510706
 [146]  1.009965978 -0.740351491  1.606696949  0.048128896  0.020056164
 [151]  0.328996323  0.718523059 -1.259203616  0.035766706 -0.349062314
 [156] -0.746769992 -0.066204738 -0.723918685  0.108238376 -1.126909148
 [161] -1.146212538  0.438357163  1.373869999 -0.475436304  1.029582330
 [166]  0.255652184  0.852984020  0.465967427  0.675679531 -1.840240398
 [171]  0.082774371 -1.671865591 -0.017715461 -1.462968102  0.853017852
 [176]  0.363678379 -1.286967843 -0.835743149 -0.602542961  0.336974613
 [181] -0.509174924 -0.396975579 -1.234531178  2.058000114  0.200429386
 [186] -0.472969067  0.646247214 -0.156592995  2.276172179 -0.625280638
 [191]  1.050034561  0.846830721 -0.495408689 -0.009804616 -0.190627963
 [196]  0.491034788 -0.187225501  0.447903453  1.197522801 -2.501486654
 [201] -0.818030914  0.272359149  0.920029122  0.461145088 -1.940946698
 [206] -0.047763843  1.196146976  0.299018503  0.092880578 -0.882720279
 [211]  0.103621246 -0.623024959 -0.627436753  0.701770310  0.556076258
 [216]  1.710957184  1.111944542 -0.543912255 -0.914056982 -0.560270125
 [221] -1.039840100  0.301023797 -0.466149447 -2.085376294  1.871109144
 [226]  1.061501981 -1.047510721  0.863648944 -0.506841139 -0.955452777
 [231] -0.393882390 -0.672546473  0.800906583 -0.795692330  1.271992094
 [236]  0.268408325  0.293176330  0.056900332 -1.474382194 -0.061279123
 [241] -0.554596282  1.435949291 -1.264238076 -0.616895755  0.618288362
 [246] -0.809451922 -1.614979734 -1.694167976 -0.036775898  0.832937070
 [251] -1.625596920  1.076186380  0.017979998  1.519526926 -0.616391060
 [256] -0.496590199  0.122388365 -0.589737672 -2.272591951 -0.737042391
 [261] -0.557142025 -1.721119163  1.080590282 -1.299858858  1.031842429
 [266] -1.218068604 -0.241141413  0.922353860 -2.046504612  1.049883992
 [271] -1.182710098  0.334203737 -0.158755779 -0.140419683  0.398282335
 [276]  1.353646311 -1.030375899  0.215143513  1.331734206 -0.615238142
 [281]  0.712635846  0.663477603  1.254592710  0.467797334  1.829445600
 [286] -2.380982874 -1.157657268  0.281190125 -0.001739929 -1.795066200
 [291] -0.243428671 -1.062173380 -0.416449913 -0.590761333  0.417667730
 [296]  1.384812587 -0.606768455  0.241215209 -2.722395101 -0.361189736
 [301] -0.670939861  0.142990835  0.258398454 -0.911111777  0.283842252
 [306] -0.022792018 -1.202433689  0.505762746 -0.876076069 -1.494288676
 [311] -1.458852579 -0.058139716 -0.647726823  0.983524386 -0.197485975
 [316]  1.217150939 -0.922081680 -0.381156931 -0.847793672  0.233317304
 [321]  0.326089005 -0.070876102 -0.845101908  0.493939924  1.441949197
 [326]  0.533420326 -1.246123575 -0.254401482  0.172348854 -0.358959694
 [331] -1.363059136  1.502754506 -1.436794739 -0.664152643 -0.260854241
 [336]  0.496996696 -0.079340344  0.202053601  0.561307774  0.879413351
 [341] -1.316307371 -0.679550205  0.785087055  0.085174301  1.357840100
 [346] -2.401153128  0.221589941 -2.561275233  0.334018504  0.138813012
 [351]  1.447930131 -0.734906506  0.200309302 -0.211635680  0.117412161
 [356]  0.215454497 -0.144057641  2.371447708 -0.504266335 -0.226521310
 [361] -1.962892139 -0.596575661 -0.006626336 -0.160740432 -0.060222719
 [366] -0.106675250 -0.063317911 -1.551119819 -2.394941299 -0.231124749
 [371]  1.148814057 -1.844225832  1.421775211 -0.270563629  1.780391503
 [376]  0.537340183 -1.591034350  0.983611507 -0.237544894 -1.025054714
 [381] -1.718665515 -1.789110195  0.469862631 -0.967071976 -0.214493586
 [386]  0.343870315  0.216105891 -1.108350854  0.181921667  0.861944104
 [391] -0.589878250 -0.302188161  0.094683565  0.751999938 -0.438402782
 [396] -0.010497856 -0.772269286 -1.054609298 -3.298686697 -1.426201135
 [401] -0.821629548  2.101655873  0.326434649 -0.208032866  0.039653102
 [406]  0.039742519 -1.309082911  0.274940509 -0.681745728 -0.289789443
 [411]  0.415823447  0.466558649  1.903177829  0.893752173 -2.162109336
 [416] -0.636245555 -0.868586187  0.102364507  0.668630865  0.254330293
 [421] -0.037429517 -0.905048003  0.215736561 -0.231461093 -1.083840892
 [426]  0.228297962 -0.405063925  1.268071227  0.802469491  0.196578956
 [431] -1.051156455 -0.501888215 -0.995845788  0.050612151  1.772827717
 [436] -0.544827113 -0.068393533 -0.882102336 -1.567978252 -0.985559413
 [441]  0.159485102 -0.568705992  1.218624578  0.788921515  1.194203164
 [446]  0.453671429 -0.568174004 -0.395380238 -0.266833956 -1.638474997
 [451] -0.420389351  1.580508655  0.536099854 -0.055304434 -1.124238396
 [456]  0.534795529  1.185026821  1.461224892  0.181658112  1.187996009
 [461] -1.079299764  1.938691715 -0.553797571  1.575429993 -0.904078828
 [466] -1.038397733 -0.017994619  0.852989266 -0.027356076  0.686366169
 [471]  0.290807534  0.290403705  0.207947520 -0.151591378  1.287767706
 [476] -0.203456062  0.762622092 -0.952493877  0.118248062  0.966520308
 [481] -0.156088391 -0.496354478 -1.158874567 -0.433248836 -0.403915639
 [486] -0.718398701 -0.791985039 -1.101340110 -0.381800459  0.897171076
 [491] -1.347350375  0.935162238  1.967283455 -1.538385737  1.785112035
 [496]  1.049032811  0.933369059  0.288096075 -0.140622921 -0.424148314
 [501]  0.800319460 -1.792970715  0.585910166  0.185232820 -0.991651168
 [506] -0.107343475  0.630473444 -0.170168872 -0.650347317 -0.931115725
 [511] -0.432579195  0.662133310 -1.122711489 -0.852861442 -1.019746031
 [516]  0.254421608  0.157941681  0.759446238 -1.868858211  0.615579479
 [521]  0.659446846 -0.326761758  1.071303872 -0.164892531 -0.975256027
 [526]  0.173903269 -0.001374182  0.414621424 -1.152009433 -1.149920978
 [531] -1.941368786 -1.193373004  0.682048852 -2.844538440 -0.880677053
 [536]  0.018046288 -1.518957677  0.228798328 -0.529367230  0.003542041
 [541]  0.934371027  0.485114580 -0.749453054 -0.254138942 -0.014167704
 [546] -0.163564465 -0.568208637  0.667836131 -1.127910963  0.126606014
 [551] -0.409560672  1.747346782 -0.848361578  0.497367152  0.245094974
 [556] -0.072951297 -0.834887712  1.007017973 -0.937129804  0.630827781
 [561] -0.071442867  2.177501372 -0.804128064  0.289301280  1.507611327
 [566] -0.868866560  0.565971814 -1.989245823 -0.521826084  2.873798818
 [571]  0.666354378 -0.755643264 -0.008323846 -0.580132422 -1.622578651
 [576]  0.384989478 -0.329619821 -0.045161456  0.811168016 -0.667414450
 [581] -0.916688985 -0.092819186  0.004963066  0.812627121  0.524054962
 [586]  0.029291541  0.868994532 -0.528108422 -0.457529632 -0.449802589
 [591] -0.717674122 -0.518509941 -0.137287414  0.311105782 -0.154753708
 [596] -0.584004630 -1.168056901  0.133741160  1.522137154  2.587816320
 [601]  0.931071393  1.467237288 -0.166783551  0.923134740  1.189186564
 [606] -1.780914233  0.438932798  0.020369747 -0.078521502  1.365501002
 [611]  1.340142132  0.066848026  0.320735783 -0.004727185  0.683329809
 [616] -0.591933989  0.026254395  0.636469400 -0.288899301 -0.116188819
 [621] -1.088273728  0.815075410 -1.241382877 -2.953593458 -1.602432456
 [626] -0.091340964  0.176864887  1.015272422  1.284430156  1.345831309
 [631] -0.577984842  1.478456622  1.607995402  1.127239384  0.776790938
 [636] -0.578359808  0.189213173  0.307185516  0.232576708  0.357473186
 [641] -0.624995215 -0.671664169  0.914025041  1.739053764  0.459450654
 [646]  1.594934698 -0.562817015 -1.330170424  0.981892111  0.102857410
 [651]  1.806908728 -1.256989209 -0.059927588 -0.515685843 -0.025789448
 [656] -0.234959104  0.140519214  0.326946682  0.179026910 -1.382276020
 [661] -0.197735833 -0.741451921  0.739271382  0.852743103 -0.507370225
 [666]  1.249105530  1.946848676 -0.009280552  1.599268669 -1.655473384
 [671]  0.656541006  1.133809996  0.424844495  1.141821357 -0.177253541
 [676]  0.842370811 -0.282547511  0.028241879  0.743962720  0.529063156
 [681] -1.327524365 -0.439840102  0.814994455 -1.429643352  0.163255747
 [686]  1.180427047  0.038067087  0.514488389  0.506152267  1.053289926
 [691]  0.348614838  0.333601692 -0.394370250  1.560453964 -0.119631297
 [696]  2.584260558  0.642638115  1.418895301  0.080662120  1.163741139
 [701]  0.918362270  0.620886138  0.878137545  1.160513447 -0.958724099
 [706] -0.232614550 -0.215065405  1.147070479  0.111047592  0.689910326
 [711] -1.026872814  0.587229707 -0.212231241 -0.633159686  0.675070793
 [716]  0.162704984  0.433213068  0.040092041 -1.089633590  1.059395383
 [721] -1.651428317 -0.539310733 -1.395872053  0.021180690  0.877132215
 [726] -1.077891673  0.064926082 -0.378188904 -1.012560492 -1.523427273
 [731]  0.276316964  0.658568521  0.030604524 -0.381134156  0.790833312
 [736]  0.785851286 -0.063217985  0.721619215  1.341935261  1.488434096
 [741] -0.037447484 -0.507230766 -1.043455730 -0.913169696  1.456858417
 [746]  0.918028263 -0.130951229  0.312091291 -1.214319247  0.906103422
 [751] -0.322164297  0.526635643  0.998317926  1.908541134  0.980796624
 [756] -0.599360177  0.534101097  1.083497555 -0.893258645 -1.935822239
 [761]  1.680533479  1.330559073 -0.174729342 -0.913318181  1.731389956
 [766] -0.313342452 -1.936211823  0.482961342  0.269069361 -1.004853193
 [771]  0.558265354 -1.464104425 -1.153482937  1.627984315 -0.393135807
 [776]  0.712746755  1.776522717  0.570739405 -0.404238519 -1.322402201
 [781] -1.727906335 -0.265038591 -0.417668170 -0.635765683 -0.799615932
 [786]  0.887490592  0.419795057  0.814217675 -0.826983669  0.263291586
 [791]  2.291364677  0.009182078 -1.850690764  0.649066409  0.122888832
 [796]  1.202085991 -1.412915457 -0.211079503  0.420215154  1.821195413
 [801]  0.251586748 -0.706562308 -1.030545485  1.109072801 -1.067205799
 [806]  1.000688438 -1.112800865 -1.774499167  0.088079379 -1.286011881
 [811] -0.918026909  0.822072370 -0.465855905 -1.194671328  1.810302236
 [816] -1.047815868  0.884776795  0.331686030  0.720832598  0.716108473
 [821] -0.620006356 -1.183011749  0.767805034 -0.147991461 -0.096494491
 [826] -1.222773163 -0.371251367 -1.641467719  0.591822076 -0.497611770
 [831]  0.689248486  2.542888336  1.216868289  0.524395975 -0.379351344
 [836] -0.359573847 -2.265194854  0.155746141  0.435160198  1.385551538
 [841]  1.080207537 -0.858382560  0.296769292  0.228351526  0.330835502
 [846] -0.157733884  1.786593794 -1.656313893 -1.531941359  0.678739963
 [851]  0.546778943 -0.661911592  1.592100410 -0.588176551 -1.096573811
 [856]  0.750960868 -0.836932201 -0.685012187  0.183252716  0.450625971
 [861]  0.479794816  1.274555408 -0.280335985  0.592887678 -1.189249146
 [866]  1.153347603  1.159255218 -1.038619094 -0.342301799 -0.244802268
 [871]  0.669159266 -2.501653021  0.487594539 -0.867594018 -0.068191330
 [876] -0.121076082 -0.773021565  2.252778176  1.589327694 -0.904656617
 [881]  1.202883587 -0.840116998 -1.405076250 -0.510774708 -1.194913915
 [886] -0.167286870  1.154128138 -0.402814335 -0.919567228 -1.321164860
 [891] -0.055343684 -1.051302967 -0.582856583 -0.572879728 -0.049227062
 [896] -0.271165547 -0.728497867  1.024241646  0.724110155  0.629550026
 [901]  0.270266913 -0.418685395  1.114870307 -1.233329963  0.247915801
 [906] -1.031430589  1.426889288  0.293721563  0.444370085 -1.278565269
 [911] -0.560444472  0.061495021 -0.245809791 -0.810250764  1.369064132
 [916]  1.069662737 -0.668225135  0.308855193  1.483751250  0.452574903
 [921] -0.593531243 -1.904148434 -0.502035808 -0.119372584 -0.182852803
 [926]  0.749276878  0.894553915  0.617794617 -1.543368385  0.890777182
 [931] -0.965267098  0.530583669  0.469063646  0.223773794  0.635072181
 [936]  0.826315412  0.587089288 -1.477048771 -0.416032435 -0.481095827
 [941] -0.350111345 -0.807395400 -2.481019521 -0.787610812 -1.433858454
 [946] -1.300209660  1.833546117 -0.136022421 -0.210545146 -1.578739933
 [951]  1.527982203 -0.119383933 -0.923432122 -1.520838638 -0.249260861
 [956]  0.767686761  0.842736884  1.474949785 -0.257706740 -0.241265862
 [961]  1.278744308  1.489405495  2.391853687  0.027776381  0.660879248
 [966]  0.280237031  1.742919813 -1.550408860  0.012568808 -0.512198326
 [971]  0.849014934  0.110245831 -1.252580454  0.832951747 -0.558961455
 [976] -1.210590890  1.296808430 -1.255183360  0.898406863 -0.076954771
 [981]  0.021064323  0.663333919 -0.115727153 -0.422118239 -0.205087514
 [986] -1.970124258  1.039532720  1.384354131  1.388133686  1.136617524
 [991] -1.440925036 -0.190583858  0.967594281 -0.077660063 -0.161247207
 [996]  0.666775125  0.821989197 -0.697498341 -0.414111988 -0.770503581

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0
  [38] 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1
  [75] 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0
 [112] 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1
 [149] 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0
 [186] 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0
 [223] 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0
 [260] 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1
 [297] 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1
 [334] 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1
 [371] 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1
 [408] 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1
 [445] 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0
 [482] 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0
 [519] 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0
 [556] 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1
 [593] 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1
 [630] 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1
 [667] 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1
 [704] 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1
 [741] 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0
 [778] 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0
 [815] 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1
 [852] 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1
 [889] 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0
 [926] 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0
 [963] 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0
[1000] 0

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   167.   78.2 Green      B    
 2     2   173.   87.3 Grey       B    
 3     3   162.   86.5 Brown      A    
 4     4   164.   73.9 Green      A    
 5     5   175.   89.0 Grey       B    
 6     6   164.   80.4 Brown      A    
 7     7   181.   85.2 Blue       B    
 8     8   169.   74.5 Green      A    
 9     9   171.   84.2 Green      B    
10    10   165.   89.8 Brown      B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups